DIPSY and HEJhome.thep.lu.se/~leif/talks/CERN11a.pdf · Introduction DIPSY HEJ ˇ Introduction DIPSY: arXiv:1103.4321 [hep-ph] Dipoles in Impact-Parameter Space and rapiditY Based

IntroductionDIPSY

HEJˇ

DIPSY and HEJnew hadron-level generators forminimum bias and jet production

Leif Lönnblad

CERN-TH andDepartment of Astronomyand Theoretical Physics

Lund University

CERN 2011.05.10

DIPSY & HEJ 1 Leif Lönnblad CERN/Lund University

IntroductionDIPSY

HEJˇ

Introduction

◮ DIPSY: arXiv:1103.4321 [hep-ph]◮ Dipoles in Impact-Parameter Space and rapiditY◮ Based on LL BFKL (Mueller dipoles)◮ Adds non-leading effects◮ Now also exclusive hadronic final states

◮ HEJ: arXiv:1104.1316 [hep-ph]◮ High Energy Jets◮ Based on (N)LL BFKL◮ Takes full kinematics into account◮ Now also exclusive hadronic final states


IntroductionDIPSY

HEJˇ

The virtual cascadeThe interaction

ˇThe Swing

DIPSY (with Christoffer Flensburg and Gösta Gustafson)


IntroductionDIPSY

HEJˇ


ˇThe Swing

The virtual cascade

Q

Q

1

0

1

0

r01

2

r12

r02

1

0

2

3

y

x

◮ Muellers formulation of BFKL

◮dPdy = α

2πd2r2

r201

r202r2

12

◮ Dipoles in impact parameter space, evolved in rapidity◮ Builds up virtual Fock-states of the proton


IntroductionDIPSY

HEJˇ


ˇThe Swing

Non-leading effects

◮ Running αs

◮ Introduce k⊥ ∼ 1/r to get energy–momentumconservation.

◮ Non-perturbative regularization with small gluon mass(confinement effects)


IntroductionDIPSY

HEJˇ


ˇThe Swing

The interaction

◮ Dipole–dipole interaction:

F =∑

ij fij fij = α2s

2 ln2(

rii′ rjj′

rij′ rji′

)

◮ Unitarize to get saturation effects (pomeron loops):F → 1 − e−F

◮ Without energy conservation we get exponential growth ofsmall dipoles which do not interact

◮ Non-perturbative regularization with small gluon mass◮ Rederive Mueller’s expression above in transverse

momentum space for final states.


IntroductionDIPSY

HEJˇ

ˆ The interactionThe Swing

ˇReal gluons

The Swing

◮ Thu unitarized interaction probability gives pomeron loopsonly in the interaction frame.

◮ To be Lorentz invariant we want them also in the evolution◮ Accomplished by the Swing (colour reconnection)◮ Two dipoles with the same colour may reconnect.◮ Does not reduce the number of dipoles, but smaller dipoles

are favoured, and these have weaker interactions.◮ In the end we get saturation in both evolution and

interaction


IntroductionDIPSY

HEJˇ

ˆ The interactionThe Swing

ˇReal gluons

We now have a model for inclusive and semi-exclusiveobservables, which includes explicit modeling of fluctuations inthe initial state

◮ pp and ep-DIS total cross section OK◮ pp and ep-DIS (quasi) elastic cross section OK

including t-dependence◮ pp and ep-DIS diffraction OK◮ Double parton scattering at the LHC — interesting

predictions

But we want fully exclusive hadronic final states


IntroductionDIPSY

HEJˇ

ˆ The SwingReal gluonsComparison with data

Real gluons

We have generated the gluonic Fock-states of the collidingprotons.

Most of the gluons in this state are simply virtual fluctuations,which will not make it to the final state.

In the momentum picture all gluons in the proton with large p+

will be off-shell with a negative p− component.

Only those gluons which actually collides (or have childrenwhich collides) with gluons from the proton with large p− will beable to come on-shell. All others must be reabsorbed.


IntroductionDIPSY

HEJˇ


But... energy–momentum conservation effects were taken intoaccount assuming all gluons were real. When some arereabsorbed the kinematics will change.

Also some sequences of emissions in the evolution willcorrespond to local hard scatterings in some frame, and thesewill not get the proper ∼ 1/q4

⊥behavior.

In the end we want to just have primary (a.k.a. backbone)gluons left, which are ordered in both q+ and q− (and hencealso in rapidity).

These are the ones we know gives the non-vanishingcontributions to the cross section.


IntroductionDIPSY

HEJˇ


◮ Choose which dipoles interact: 1 − e−Fij

◮ Take away non-interacting gluons◮ Take away kinematically impossible interactions/gluons◮ Take away wrongly distributed sub-scatterings◮ Take away non-ordered gluons


IntroductionDIPSY

HEJˇ


Final state radiation and hadronization

The primary gluons are now sent to ARIADNE for final-stateshowering.

This is a unitary procedure and only emissions which areunordered in q+ and q− w.r.t. the primary gluons are allowed.

Then we send everything to PYTHIA8 for hadronization.


IntroductionDIPSY

HEJˇ


Frame-independence

We have quite a lot of parameters:

◮ Rmax: Non-perturbative regularization◮ Rp: Proton size (≈ Rmax)◮ wp: Fluctuations in the initial proton size (small)◮ ΛQCD: in the running αs

◮ λr : Swing parameter (saturated)

Most of these can be fit to the total and elastic cross sections.

But there are also a lot of choices made for which no guidancecan be found in perturbative QCD, especially for the selection ofthe real gluons.

Most of these can be fixed by requiring frame-independence.


IntroductionDIPSY

HEJˇ


Comparison with datab b b b b b b b b b b b b b b b b b

bbbbb b

bb

b

b

b

× × × × × × × × × × × × × × × × × × × × × × × × × × ××

×ATLAS datab

DIPSY

Pythia8

Pythia8(ND)

DIPSY(asym)×

10−6

10−5

10−4

10−3

10−2

10−1

Charged multiplicity ≥ 6 at 900 GeV, track p⊥ > 500 MeV

1/

σd

σ/

dN

ch

× × × × × × × × × × × × × × × × × × × × ×× ×

10 15 20 25 30 35 40 45

0.6

0.8

1

1.2

1.4

Nch

MC

/d

ata

More plots on http://home.thep.lu.se/∼leif/DIPSY.html


IntroductionDIPSY

HEJˇ


b b b b b b b b b b b b b b b b b b b b b b b b b b bb

b

b

b

b

b

b

××××××××××××××××××××××××××× ××

××

×

×

×

ATLAS datab

DIPSY

Pythia8

Pythia8(ND)

DIPSY(asym)×

10−6

10−5

10−4

10−3

10−2

10−1

Charged multiplicity ≥ 6 at 7 TeV, track p⊥ > 500 MeV

1/

σd

σ/

dN

ch

×××××××

×××××××××××××××××××× × × ×

×

×

20 40 60 80 100 120

0.6

0.8

1

1.2

1.4

Nch

MC

/d

ata


IntroductionDIPSY

HEJˇ


bb

bb b b b b b b b b b b b b b b b b b

bbbb

bb

b

bb

bb

b

b

b

b

× × × × × ××××××××××××××××××× × × × × × × × ××

××

×

ATLAS datab

DIPSY

Pythia8

Pythia8(ND)

DIPSY(asym)×

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

1

Charged particle p⊥ at 7 TeV, track p⊥ > 500 MeV, for Nch ≥ 6

1/

Nev

1/

2π

p⊥

dσ

/d

ηd

p⊥

× × × ××

×××××××××××××

××××

×××

×

1 10 1

0.6

0.8

1

1.2

1.4

p⊥ [GeV]

MC

/d

ata


IntroductionDIPSY

HEJˇ


b b b b b b bb b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

b b b bbb

××××××××××××××××××××××××××××××××××××××××××××××××××

ATLAS datab

DIPSY

Pythia8

Pythia8(ND)

DIPSY(asym)×

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5Charged particle η at 900 GeV, track p⊥ > 500 MeV, for Nch ≥ 6

1/

Nev

dN

ch/

dη

××××××××××××××××××××××××××××××××××××××××××××××××××

-2 -1 0 1 2

0.6

0.8

1

1.2

1.4

η

MC

/d

ata


IntroductionDIPSY

HEJˇ


bb b b

b b bb b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

b b bb b b

b

××××××××××××××××××××××××××××××××××××××××××××××××××

ATLAS datab

DIPSY

Pythia8

Pythia8(ND)

DIPSY(asym)×

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5Charged particle η at 7 TeV, track p⊥ > 500 MeV, for Nch ≥ 6

1/

Nev

dN

ch/

dη

××××××××××××××××××××××××××××××××××××××××××××××××××

-2 -1 0 1 2

0.6

0.8

1

1.2

1.4

η

MC

/d

ata


IntroductionDIPSY

HEJˇ


Valence configuration

In general the description of data is worse than for PYTHIA8(Tune 4c), but better than most other generators(c.f. mcplots.cern.ch).

One main problem is the naive valence configuration used: wemay get very high energy gluons interacting and giving too hardjets in the forward region. (We’re working on it).


IntroductionDIPSY

HEJˇ


Heavy Ions

DIPSY can also be used for heavy-ion collisions.

This give us a model of possible fluctuations and correlations inthe initial state gluon distribution necessary to understandpossible hydrodynamical and other collective effects in the finalstate.

(DIPSY is a bit too slow right now, ∼ 30min for an LHC event)


DIPSYˆHEJ

Summary

Matching to a collinear showerJet shapes

ˇFuture Developments

HEJ - High Energy Jets(with Jeppe Andersen and Jennifer Smillie)

From Minimum Bias to Jet production. . .

HEJ is basically a Matrix Element generator (à la MadEvent)with a perturbative approximation of jet production to any orderof αs.

The predictions are exact in the limit of large invariant massbetween all partons (BFKL). And is matched to MadGraph forlow parton multiplicities.


DIPSYˆHEJ

Summary



The typical process: f1f2 → f1g · · ·gf2

σresum,match2j =

∑

f1,f2

∞∑

n=2

n∏

i=1

(∫ pi⊥=∞

pi⊥=λ

d2p i⊥

(2π)3

∫

dyi

2

)

|Mf1f2→f1g···gf2HEJ ({pi})|

2

s2

×∑

m

Oemj({pi}) wm−jet

× xafA,f1(xa, Qa) x2fB,f2(xb, Qb) (2π)4 δ2

(

n∑

i=1

p i⊥

)

O2j({pi})

Resum to all-orders the leading logarithmic virtual correctionsto the t-channel poles.


DIPSYˆHEJ

Summary



Matching to a collinear shower

As with all matrix element generators, we want to add partonshowers and hadronization to get fully simulated final states.And we must be careful not to double count!

How do we do that here, where HEJ already resums sometowers of logarithms?

◮ Parton Shower: soft and collinear resummation◮ HEJ: soft resummation (not exactly the same as in the PS).


DIPSYˆHEJ

Summary



We will simply send the partonic state generated by HEJ toARIADNE and start the shower.

For each emission, we send back the state to HEJ and ask,Hej! How would you have done this emission?

The dipole splitting function in ARIADNE is an approximation tothe ratio of matrix elements

DAri(p2⊥, y) ≈

z16π2

|Mn+1|2

|Mn|2 .

From this we simply subtract the corresponding HEJ calculation

DHEJ(p2⊥, y) =

z16π2

∣

∣MHEJn+1

∣

∣

2

∣

∣MHEJn

∣

∣

2 .


DIPSYˆHEJ

Summary



We veto the ARIADNE emission with probability DHEJ/DAri in away such that the collinear logarithms are still resumed in theSudakov form factors. (c.f. the Veto algorithm)

(wrt. beam) [GeV]k0 10 20 30 40 50 60

]-2

<Spl

it> [G

eV

-510

-410

-310

-210

-110

1

HEJ

Ariadne

r0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

]-2

<Spl

it> [G

eV

-410

-310

-210

HEJ

Ariadne


DIPSYˆHEJ

Summary



Jet shapes

-5 -4 -3 -2 -1 0 1 2 3 4 5

-3-2

-10

12

30

1020304050607080

HEJ partons

Particles after showerRapidity

φ

(GeV)p


DIPSYˆHEJ

Summary



r0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

to

t /

p(r

) =

pρ

-110

1

10

)=(1.64,2.02)φ(y,

)=(-3.535,1.817)φ(y,


DIPSYˆHEJ

Summary



1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

ρ(r)

r

ATLAS jet profiles

160 < p⊥ < 210 (x35)

110 < p⊥ < 160 (x34)

80 < p⊥ < 110 (x33)

60 < p⊥ < 80 (x32)

40 < p⊥ < 60 (x31)

30 < p⊥ < 40

ATLASHEJ+Ariadne

Pythia P10Pythia P10 (no MI)


DIPSYˆHEJ

Summary

ˆ Jet shapesFuture Developments

Future Developments

For very hard jets there is still a problem that the existence ofsoft gluons from HEJ close to the jet, prevents ARIADNE fromemitting enough collinear radiation, making the jets a bit toonarrow.

We’re working on that...


DIPSYˆHEJ

Summary

Summary

◮ Two new BFKL-based hadron-level generators◮ DIPSY: Minimum Bias and Heavy Ions◮ HEJ: Jets


DIPSYˆHEJ

Summary


Documents

DIPSY and HEJhome.thep.lu.se/~leif/talks/CERN11a.pdf · Introduction DIPSY HEJ ˇ Introduction DIPSY: arXiv:1103.4321 [hep-ph] Dipoles in Impact-Parameter Space and rapiditY Based